Evaluating Large Vision-and-Language Models on Children's Mathematical Olympiads

Recent years have seen a significant progress in the general-purpose problem solving abilities of large vision and language models (LVLMs), such as ChatGPT, Gemini, etc.; some of these breakthroughs even seem to enable AI models to outperform human abilities in varied tasks that demand higher-order cognitive skills. Are the current large AI models indeed capable of generalized problem solving as humans do? A systematic analysis of AI capabilities for joint vision and text reasoning, however, is missing in the current scientific literature. In this paper, we make an effort towards filling this gap, by evaluating state-of-the-art LVLMs on their mathematical and algorithmic reasoning abilities using visuo-linguistic problems from children's Olympiads. Specifically, we consider problems from the Mathematical Kangaroo (MK) Olympiad, which is a popular international competition targeted at children from grades 1-12, that tests children's deeper mathematical abilities using puzzles that are appropriately gauged to their age and skills. Using the puzzles from MK, we created a dataset, dubbed SMART-840, consisting of 840 problems from years 2020-2024. With our dataset, we analyze LVLMs power on mathematical reasoning; their responses on our puzzles offer a direct way to compare against that of children. Our results show that modern LVLMs do demonstrate increasingly powerful reasoning skills in solving problems for higher grades, but lack the foundations to correctly answer problems designed for younger children. Further analysis shows that there is no significant correlation between the reasoning capabilities of AI models and that of young children, and their capabilities appear to be based on a different type of reasoning than the cumulative knowledge that underlies children's mathematics and logic skills.

Gear-NeRF: Free-Viewpoint Rendering and Tracking with Motion-aware Spatio-Temporal Sampling

Extensions of Neural Radiance Fields (NeRFs) to model dynamic scenes have enabled their near photo-realistic, free-viewpoint rendering. Although these methods have shown some potential in creating immersive experiences, two drawbacks limit their ubiquity: (i) a significant reduction in reconstruction quality when the computing budget is limited, and (ii) a lack of semantic understanding of the underlying scenes. To address these issues, we introduce Gear-NeRF, which leverages semantic information from powerful image segmentation models. Our approach presents a principled way for learning a spatio-temporal (4D) semantic embedding, based on which we introduce the concept of gears to allow for stratified modeling of dynamic regions of the scene based on the extent of their motion. Such differentiation allows us to adjust the spatio-temporal sampling resolution for each region in proportion to its motion scale, achieving more photo-realistic dynamic novel view synthesis. At the same time, almost for free, our approach enables free-viewpoint tracking of objects of interest - a functionality not yet achieved by existing NeRF-based methods. Empirical studies validate the effectiveness of our method, where we achieve state-of-the-art rendering and tracking performance on multiple challenging datasets.

TI2V-Zero: Zero-Shot Image Conditioning for Text-to-Video Diffusion Models

Text-conditioned image-to-video generation (TI2V) aims to synthesize a realistic video starting from a given image (e.g., a woman's photo) and a text description (e.g., "a woman is drinking water."). Existing TI2V frameworks often require costly training on video-text datasets and specific model designs for text and image conditioning. In this paper, we propose TI2V-Zero, a zero-shot, tuning-free method that empowers a pretrained text-to-video (T2V) diffusion model to be conditioned on a provided image, enabling TI2V generation without any optimization, fine-tuning, or introducing external modules. Our approach leverages a pretrained T2V diffusion foundation model as the generative prior. To guide video generation with the additional image input, we propose a "repeat-and-slide" strategy that modulates the reverse denoising process, allowing the frozen diffusion model to synthesize a video frame-by-frame starting from the provided image. To ensure temporal continuity, we employ a DDPM inversion strategy to initialize Gaussian noise for each newly synthesized frame and a resampling technique to help preserve visual details. We conduct comprehensive experiments on both domain-specific and open-domain datasets, where TI2V-Zero consistently outperforms a recent open-domain TI2V model. Furthermore, we show that TI2V-Zero can seamlessly extend to other tasks such as video infilling and prediction when provided with more images. Its autoregressive design also supports long video generation.

Equivariant Spatio-Temporal Self-Supervision for LiDAR Object Detection

Popular representation learning methods encourage feature invariance under transformations applied at the input. However, in 3D perception tasks like object localization and segmentation, outputs are naturally equivariant to some transformations, such as rotation. Using pre-training loss functions that encourage equivariance of features under certain transformations provides a strong self-supervision signal while also retaining information of geometric relationships between transformed feature representations. This can enable improved performance in downstream tasks that are equivariant to such transformations. In this paper, we propose a spatio-temporal equivariant learning framework by considering both spatial and temporal augmentations jointly. Our experiments show that the best performance arises with a pre-training approach that encourages equivariance to translation, scaling, and flip, rotation and scene flow. For spatial augmentations, we find that depending on the transformation, either a contrastive objective or an equivariance-by-classification objective yields best results. To leverage real-world object deformations and motion, we consider sequential LiDAR scene pairs and develop a novel 3D scene flow-based equivariance objective that leads to improved performance overall. We show our pre-training method for 3D object detection which outperforms existing equivariant and invariant approaches in many settings.

Multimodal 3D Object Detection on Unseen Domains

LiDAR datasets for autonomous driving exhibit biases in properties such as point cloud density, range, and object dimensions. As a result, object detection networks trained and evaluated in different environments often experience performance degradation. Domain adaptation approaches assume access to unannotated samples from the test distribution to address this problem. However, in the real world, the exact conditions of deployment and access to samples representative of the test dataset may be unavailable while training. We argue that the more realistic and challenging formulation is to require robustness in performance to unseen target domains. We propose to address this problem in a two-pronged manner. First, we leverage paired LiDAR-image data present in most autonomous driving datasets to perform multimodal object detection. We suggest that working with multimodal features by leveraging both images and LiDAR point clouds for scene understanding tasks results in object detectors more robust to unseen domain shifts. Second, we train a 3D object detector to learn multimodal object features across different distributions and promote feature invariance across these source domains to improve generalizability to unseen target domains. To this end, we propose CLIX$^\text{3D}$, a multimodal fusion and supervised contrastive learning framework for 3D object detection that performs alignment of object features from same-class samples of different domains while pushing the features from different classes apart. We show that CLIX$^\text{3D}$ yields state-of-the-art domain generalization performance under multiple dataset shifts.

G-RepsNet: A Fast and General Construction of Equivariant Networks for Arbitrary Matrix Groups

Group equivariance is a strong inductive bias useful in a wide range of deep learning tasks. However, constructing efficient equivariant networks for general groups and domains is difficult. Recent work by Finzi et al. (2021) directly solves the equivariance constraint for arbitrary matrix groups to obtain equivariant MLPs (EMLPs). But this method does not scale well and scaling is crucial in deep learning. Here, we introduce Group Representation Networks (G-RepsNets), a lightweight equivariant network for arbitrary matrix groups with features represented using tensor polynomials. The key intuition for our design is that using tensor representations in the hidden layers of a neural network along with simple inexpensive tensor operations can lead to expressive universal equivariant networks. We find G-RepsNet to be competitive to EMLP on several tasks with group symmetries such as O(5), O(1, 3), and O(3) with scalars, vectors, and second-order tensors as data types. On image classification tasks, we find that G-RepsNet using second-order representations is competitive and often even outperforms sophisticated state-of-the-art equivariant models such as GCNNs (Cohen & Welling, 2016a) and E(2)-CNNs (Weiler & Cesa, 2019). To further illustrate the generality of our approach, we show that G-RepsNet is competitive to G-FNO (Helwig et al., 2023) and EGNN (Satorras et al., 2021) on N-body predictions and solving PDEs, respectively, while being efficient.

Steered Diffusion: A Generalized Framework for Plug-and-Play Conditional Image Synthesis

Conditional generative models typically demand large annotated training sets to achieve high-quality synthesis. As a result, there has been significant interest in designing models that perform plug-and-play generation, i.e., to use a predefined or pretrained model, which is not explicitly trained on the generative task, to guide the generative process (e.g., using language). However, such guidance is typically useful only towards synthesizing high-level semantics rather than editing fine-grained details as in image-to-image translation tasks. To this end, and capitalizing on the powerful fine-grained generative control offered by the recent diffusion-based generative models, we introduce Steered Diffusion, a generalized framework for photorealistic zero-shot conditional image generation using a diffusion model trained for unconditional generation. The key idea is to steer the image generation of the diffusion model at inference time via designing a loss using a pre-trained inverse model that characterizes the conditional task. This loss modulates the sampling trajectory of the diffusion process. Our framework allows for easy incorporation of multiple conditions during inference. We present experiments using steered diffusion on several tasks including inpainting, colorization, text-guided semantic editing, and image super-resolution. Our results demonstrate clear qualitative and quantitative improvements over state-of-the-art diffusion-based plug-and-play models while adding negligible additional computational cost.

Tensor Factorization for Leveraging Cross-Modal Knowledge in Data-Constrained Infrared Object Detection

The primary bottleneck towards obtaining good recognition performance in IR images is the lack of sufficient labeled training data, owing to the cost of acquiring such data. Realizing that object detection methods for the RGB modality are quite robust (at least for some commonplace classes, like person, car, etc.), thanks to the giant training sets that exist, in this work we seek to leverage cues from the RGB modality to scale object detectors to the IR modality, while preserving model performance in the RGB modality. At the core of our method, is a novel tensor decomposition method called TensorFact which splits the convolution kernels of a layer of a Convolutional Neural Network (CNN) into low-rank factor matrices, with fewer parameters than the original CNN. We first pretrain these factor matrices on the RGB modality, for which plenty of training data are assumed to exist and then augment only a few trainable parameters for training on the IR modality to avoid over-fitting, while encouraging them to capture complementary cues from those trained only on the RGB modality. We validate our approach empirically by first assessing how well our TensorFact decomposed network performs at the task of detecting objects in RGB images vis-a-vis the original network and then look at how well it adapts to IR images of the FLIR ADAS v1 dataset. For the latter, we train models under scenarios that pose challenges stemming from data paucity. From the experiments, we observe that: (i) TensorFact shows performance gains on RGB images; (ii) further, this pre-trained model, when fine-tuned, outperforms a standard state-of-the-art object detector on the FLIR ADAS v1 dataset by about 4% in terms of mAP 50 score.

Pixel-Grounded Prototypical Part Networks

Prototypical part neural networks (ProtoPartNNs), namely PROTOPNET and its derivatives, are an intrinsically interpretable approach to machine learning. Their prototype learning scheme enables intuitive explanations of the form, this (prototype) looks like that (testing image patch). But, does this actually look like that? In this work, we delve into why object part localization and associated heat maps in past work are misleading. Rather than localizing to object parts, existing ProtoPartNNs localize to the entire image, contrary to generated explanatory visualizations. We argue that detraction from these underlying issues is due to the alluring nature of visualizations and an over-reliance on intuition. To alleviate these issues, we devise new receptive field-based architectural constraints for meaningful localization and a principled pixel space mapping for ProtoPartNNs. To improve interpretability, we propose additional architectural improvements, including a simplified classification head. We also make additional corrections to PROTOPNET and its derivatives, such as the use of a validation set, rather than a test set, to evaluate generalization during training. Our approach, PIXPNET (Pixel-grounded Prototypical part Network), is the only ProtoPartNN that truly learns and localizes to prototypical object parts. We demonstrate that PIXPNET achieves quantifiably improved interpretability without sacrificing accuracy.

Are Deep Neural Networks SMARTer than Second Graders?

Recent times have witnessed an increasing number of applications of deep neural networks towards solving tasks that require superior cognitive abilities, e.g., playing Go, generating art, question answering (such as ChatGPT), etc. Such a dramatic progress raises the question: how generalizable are neural networks in solving problems that demand broad skills? To answer this question, we propose SMART: a Simple Multimodal Algorithmic Reasoning Task and the associated SMART-101 dataset, for evaluating the abstraction, deduction, and generalization abilities of neural networks in solving visuo-linguistic puzzles designed specifically for children in the 6-8 age group. Our dataset consists of 101 unique puzzles; each puzzle comprises a picture and a question, and their solution needs a mix of several elementary skills, including arithmetic, algebra, and spatial reasoning, among others. To scale our dataset towards training deep neural networks, we programmatically generate entirely new instances for each puzzle while retaining their solution algorithm. To benchmark the performance on the SMART-101 dataset, we propose a vision and language meta-learning model using varied state-of-the-art backbone neural networks. Our experiments reveal that while powerful deep models offer reasonable performances on puzzles that they are trained on, they are not better than random accuracy when analyzed for generalization. We also evaluate the recent ChatGPT large language model on a subset of our dataset and find that while ChatGPT produces convincing reasoning abilities, the answers are often incorrect.